where \(\mathbf {X} \in \mathbb {R}^{N\times K}\)  is the input feature, \(N=H\times W\)  is the number of pixel grids within the ROI region and \(K\)  is the feature dimension for each node, \(\mathbf {A} \in \mathbb {R}^{N\times N}\)  is the adjacency matrix for defining neighboring relations of graph nodes by feature similarities, and \(\mathbf {W}_g \in \mathbb {R}^{K\times K^{\prime }}\)  is the learnable weight matrix for the output transform, where \(K^{\prime }=K\)  in our case. The output feature \(\mathbf {Z} \in \mathbb {R}^{N\times K^{\prime }}\)  consists of the updated node feature by global information propagation within the whole graph layer, which is obtained after non-linear functions \(\mathbf {\sigma }(\cdot )\)  including layer normalization [1]} and ReLU functions. We add a residual connection after the GCN layer.
